acid as a coadsorbate. The maximum values achieved are ~3.5% without CA and ~4%
with CA.
steep, which has also been suggested in a previous report136 and will be confirmed for a separate set of samples in chapter 7. Comparing the solar cells with (prepared at Gifu University) and without (prepared at University of Gießen) cholic acid, the former ex-hibited a smaller α value than the latter.
Table 9: Trap distribution parameters α and relative conduction band edge shifts ΔEc/q for the different ZnO/D149 solar cells (positive ΔEc/q correspond to downward shifts, negative values correspond to upward shifts). Values represent averages obtained from one to three identically prepared samples, with the maximum difference between indi-vidual values and average given as an error estimate.
tads / min α (+/- 0.06) ΔEc/q (+/- 15) / mV
with CA (Gifu)
1 0.24 - 11
2 0.18 0 (ref.)
10 0.17 - 24
120 0.18 - 17
without CA (Gießen)
1 0.37 + 33
2 0.36 + 37
10 0.33 + 40
120 0.27 + 34
As directly apparent from the plot of the density of states g(qVf) = g(Efn) (calculated from Cµ according to eq. (44)) in Figure 42, this means that the trap distribution in the cells with D149/CA (Gifu) was higher than in the D149 samples prepared in Gießen. As a result, in the energy range qVf > 0.55 eV the density of states in the former was gener-ally reduced by about 50% compared to the latter. The steeper trap distribution in the cells prepared in Gifu was either related to the presence of cholic acid molecules, which could have reduced the density of certain surface traps by binding to coordinatively un-saturated surface sites, or it was the result of the fact that the ZnO films were aged for a shorter time than the ones used in Gießen (cf. chapter 4, Figure 36). Increasing the ad-sorption time in samples with CA from 1 minute to 120 minutes caused a small addi-tional decrease of g(Efn), indicating that the effect was at least in part caused by
coad-sorption of CA (and thus became stronger when the amount of CA was increased by increase of the adsorption time).
Figure 42: Density of states of ZnO/D149 cells (color and symbol code as in previous figures). Reprinted from ref. 278, Copyright 2013, with permission from Elsevier.
In cells without cholic acid, on the other hand, no significant influence of the soaking time can be noticed, suggesting that the density of states is largely independent of the amount of D149. While the nature of surface states in dye-sensitized solar cells is still subject of investigations, it is known that anchoring molecules to semiconductor surfac-es can entail a reduction of the density of surface traps or a change of their energetic distribution compared to bare surfaces (cf. chapter 1.1.2).68-70, 90 For instance, a dipole-induced shift has been observed upon adsorption of dyes with carboxylic acid functions to TiO2.70 Cholic acid does have a carboxylic acid group that acts as anchoring group for adsorption to the semiconductor surface. Thus, its possible influence on the density of states could have been caused by a dipole effect. On the other hand, D149 possesses a carboxylic acid function as well, but did not show any notable effect on g(Efn). This may indicate that the dipole moment associated with the carboxylic acid group of D149 did not have a strong effect on the ZnO energy levels, which likely resulted from a rela-tively weak interaction between D149 and ZnO, as reported in earlier studies on indo-line dye-sensitized ZnO.286
The fact that in the presently discussed experimental series the trap distribution parame-ter α varied between cells fabricated with different parameters precludes a reliable and exact determination of relative shifts of the conduction band edge ∆Ec/q according to
the procedure illustrated in Figure 16 (chapter 1.4.4). Nevertheless, approximate values were obtained to enable a discussion of a range of possible conduction band edge shifts (Table 9). Figure 43 demonstrates the approximate alignment across a limited voltage range resulting from shifts of the curves by these estimated ∆Ec/q values.
Figure 43: Chemical capacitance curves of the D149-sensitized ZnO solar cells shifted along the voltage axis by ∆Ec/q (Table 9), resulting in approximate alignment in the voltage range -0.55 V to -0.7 V. Due to the different slopes of the curves, no complete alignment could be achieved and the shifts ∆Ec/q merely represent rough estimations of the relative conduction band edge shifts. Reprinted from ref. 278, Copyright 2013, with permission from Elsevier.
A possible upward shift of the conduction band edge by about 40 – 60 mV is indicated in the cells containing CA with respect to the cells without coadsorbate (Table 9), with a tendency of higher shifts for the cells prepared with longer adsorption times (10 min, 120 min). A similar trend is suggested by the Vf vs. g(Efn) plots in Figure 42, which approach different saturation voltages. Accounting for the estimated error of +/- 15 mV, the approximation obtained here would be roughly comparable to the upward shift of the conduction band edge by 80 mV previously observed for TiO2-based DSCs with Ru(II) sensitizers upon coadsorption of chenodeoxycholic acid, a derivative of CA.149 An upward shift of the conduction band edge in the cells with CA, in particular at high dye loadings, thus may have contributed (via eq. (34)) to the fact that the Voc at a given dye loading was constant in the presence or absence of CA in spite of the lower rates of charge injection in the cells with coadsorbate (chapter 5.2). Since an upward shift of the
conduction band edge can cause a reduction in the electron injection efficiency (cf. sec-tion 1.1.2), these results may also deliver an explanasec-tion for the decreased slope of the short-circuit current density in cells with CA (cf. Figure 40).
5.3.2 Recombination
The EIS-based recombination resistance Rrec of the ZnO/D149 solar cells shows an ex-ponential decrease as Vf becomes more negative, Figure 44 (a), as expected for nanostructured semiconductors based on eq. (53).
Figure 44: Recombination resistance of D149-sensitized solar cells with (solid sym-bols) or without (open symsym-bols) cholic acid. (a) Rrec as a function of the Fermi-level voltage Vf, together with linear fits; (b) Rrec vs. the density of states g(Efn) (lines are a guide to the eye only). Increasing color depth represents increasing adsorption time as in the figures above. Reprinted from ref. 278, Copyright 2013, with permission from Elsevier.
As explained in detail in section 1.4.4, the recombination resistance at a given voltage of a set of samples under comparison can only be used as a measure of the probability of interfacial recombination events if the samples exhibit the same conduction band edge position Ec and the same recombination parameter β (see below), or if they show the same β and are plotted against Vf-ΔEc/q, cf. eq. (54). The physical origin behind this approach is that, at a given Fermi-level voltage, samples with different Ec and β would show different relative occupancies of trap and conduction band states, which has an effect on the total rate of recombination and would mask possible differences of Rrec
caused solely by differences in the interfacial rate constant of recombination. In the
pre-sent case, the analysis of Rrec is complicated by two factors: (1) a reliable determination of ΔEc/q was precluded due to the variations in the trap distribution between differently fabricated cells; (2) the slope of the Rrec vs. Vf curves (and, hence, β) is not constant ei-ther (Figure 44 (a)). Some previous studies have intended to avoid such complications by plotting the effective electron lifetime τn of cells with different trap distributions as a function of the total density of states g(Efn) or the total electron density n instead of ana-lyzing Rrec as a function of Vf-ΔEc/q.57, 136 To formally confirm the validity of this ap-proach, the dependence of τn on density of states and electron density according to the multiple-trapping model (cf. eq. (47), (18), (9) and (10) as well as ref. 90) is considered:
1
1) (
)
(
rcb rss
c ss t
cb r r cb fn
t fn f c µ t rec
n k k
n k n
E k g
E g n
C n
R
(74)
where nt and nc are the density of trapped and conduction band electrons, τf is the free-electron lifetime describing recombination without the influence of bulk trapping but including the influence of surface state-mediated recombination, gt(Efn) and gcb(Efn) are the densities of states of trapped and conduction band electrons (assumed to be expo-nential to obtain the last part of the equation), and krcb and krss are the rate constants for recombination from the conduction band or from surface states. In combination with eq.
(1), eq. (74) shows that a plot of τn vs. g(Efn) ≈ gt(Efn) or Rrec vs. g(Efn) ≈ gt(Efn) (cf. eq.
(45)) will only adequately reveal sample-to-sample differences in the interfacial rate constants for recombination if gcb(Efn), determined by the effective density of states at the conduction band edge Nc, is constant in the samples under comparison. Nc depends on the effective electron mass in the conduction band and is a (temperature-dependent) material constant.63 As the present experiments all used the same ZnO structures with the only difference being different surface modifications, it is expected that gcb(Efn)was equal for the series of cells studied here and, hence, Rrec is plotted as a function of the measured density of states in Figure 44 (b).IV In the range of g(Efn) ≥ 1.5·10-19 eV-1cm-3, the recombination resistance increases with increasing adsorption time (i.e., dye load-ing) for both groups of cells, with and without coadsorbate. Comparison with Figure 40 and Figure 42 shows that this range of the density of states includes the g(Efn) observed
under open-circuit conditions. Based on the above considerations, the increase in Rrec
reflects a decrease of either or both of the rate constants for recombination from conduc-tion band states or surface states, which should be related to the increased average spac-ing between semiconductor and electrolyte in the presence of the adsorbed dye entailspac-ing a reduced electronic coupling between the two phases (cf. eq. (17)). With the conduc-tion band edge posiconduc-tion being largely independent of the adsorpconduc-tion time (Table 9), the slower recombination kinetics at higher g(Efn) by increase of the dye loading delivers a partial explanation of the increase of Voc with the dye loading (cf. Figure 40), while the remaining increase resulted from the increase in Jsc (eq. (34)). Moving towards smaller densities of states in the range g(Efn) < 1.5·10-19 eV-1cm-3 (corresponding to voltages less negative than Voc), the improvement of the recombination resistance with the dye loading at a given g(Efn) becomes notably weaker until the trend is even reversed for g(Efn) ≈ 0.5·10-19 eV-1cm-3. At these lowest levels of the quasi-Fermi level, Rrec tends to be smaller in samples prepared with longer adsorption times than in those with shorter adsorption times. The observed inversion is connected to a variation of the slope of the recombination resistance curves with the dye loading (Figure 44 (a)), which will be discussed in the following section. By comparing the Rrec of cells prepared with a given adsorption time with and without coadsorbate, it can be seen that for g(Efn) ≥ 2.5·10-19 eV-1cm-3 recombination is stronger in samples with CA than in those without CA. Tak-ing into account that, in the present set of samples, the dye loadTak-ing in cells with coad-sorbate was higher than in those without CA (Table 8) and that a blocking effect of D149 on recombination in the range of high g(Efn) was detected as discussed above, the difference between samples with and without coadsorbate is probably not related to the difference in the dye loadings. Rather, it indicates that CA may have a catalytic effect on recombination at high levels of Efn. A comparable effect was seen upon coadsorption of chenodeoxycholic acid in DSCs based on Ru(II) dye-sensitized TiO.149 Nevertheless, the present cells containing the coadsorbate showed comparable open-circuit voltages at a given dye loading as cells without CA (cf. Figure 40). Thus, the higher open-circuit rate constant of recombination as well as the lower rate of charge injection for cells with
IV Note that the common procedure of plotting τn vs. n ≈ nt is only valid for an evaluation of rate constants of recombination if samples with the same trap distribution parameter α are compared and therefore is not an option for the present samples.
larger dye loadings (Figure 40) in the samples with CA must both have been compen-sated by a gain in Voc resulting from the presumed upward shift of the conduction band edge of up to ~60 mV (Table 8). With decreasing density of states below 2.5·10-19 eV
-1cm-3, the Rrec curves of the cells with CA intersect with the ones of samples without CA and, hence, the recombination resistance becomes higher in the cells with coadsorbate.
This means that under conditions of low electron densities in the semiconductor the effect of cholic acid is to reduce recombination with respect to DSCs without CA, which is likely the consequence of the anti-aggregation effect of the coadsorbate, as will be discussed in more depth below.
5.3.3 Voltage-Dependence of the Recombination Resistance
The recombination parameters β of the ZnO/D149-based DSCs, obtained from fits of the voltage-dependent recombination resistance (Figure 44 (a)) to eq. (53), showed val-ues between 0.35 and 0.53 (Figure 45), which is slightly lower than the valval-ues of 0.45 to 0.64 previously reported for D149-sensitized ZnO.136, 141.
Figure 45: Dependence of the recombination parameter β on the integrated absorbance (representing the dye loading) of ZnO/D149 DSCs with (filled symbols) and without (open symbols) cholic acid (data points represent averages of one to three individual values per preparation condition). Reprinted from ref. 278, Copyright 2013, with permis-sion from Elsevier.
β clearly decreased with increasing dye loading, with a significant difference in slope depending on the presence of the coadsorbate: Cells that did not contain CA exhibited a strong decrease of the recombination parameter by approximately 30% over the range of dye loadings studied, while in DSCs with cholic acid β was only reduced by 10%, even though the maximum dye loading achieved in those cells was higher than in the series without CA. The fact that the flattening of the voltage-dependent Rrec curves with in-creasing amount of D149 was less pronounced in the cells with cholic acid may indicate that the coadsorbate counteracted the dye-related increase of recombination at lower voltages (cf. Figure 44).
The voltage dependence of the recombination resistance is generally determined by charge transfer from a distribution of surface states in the semiconductor. It has been derived that β can be expressed as β = 0.5+αss, where αss is the trap distribution parame-ter of surface states.90 Based on this, a correlation between β and the measured trap dis-tribution parameter α, which reflects an average of the trap disdis-tributions in the bulk and at the surface, was expected. However, the samples containing cholic acid showed gen-erally lower values of α than their coadsorbate-free counterparts (Table 9), while β at high dye loadings was higher with respect to cells without CA. Moreover, the amount of dye was not found to influence α, whereas it had a considerable effect on β. Thus, in the cells investigated in this study, the voltage dependence of the recombination re-sistance did not seem to correlate with the energy distribution of electronic states in the dye-sensitized porous ZnO film. This suggests that it was rather the distribution of elec-trolyte acceptor states that controlled how the recombination rate changed with Efn. The fact that the drop in β and FF is less pronounced in the cells with cholic acid, in which D149 was less aggregated (Figure 37), suggests that the dye-related increase of the re-combination rate at lower voltages is mainly caused by D149 in aggregates.
5.3.4 Origins of the Variations of the Fill Factor
The experimental external fill factor FF is generally influenced by the series resistance as well as by Voc and β (cf. eq. (35)). Comparison of the internal fill factors FFint,exp (de-termined from the internal J-V curves in Figure 39) with FF(Table 10) reveals that in the present set of samples the series resistance lowered the fill factor by up to 10%, as discussed in more detail below. Theoretical fill factors FFint,calc expected based on the
experimental Voc and β values were calculated using the corresponding full expression of the β-recombination model (eq. (26) of ref. 128), see Table 10.
Table 10: Experimental internal and external fill factors, FF and FFint,exp, as well as theoretical internal fill factors FFint,calc for ZnO/D149 solar cells with different dye loadings, represented by the integrated absorbance absint.
absint (+/- 16) / nm FF FFint,exp FFint,calc
with CA (Gifu)
92 0.66 0.69 0.71
124 0.63 0.66 0.71
303 0.59 0.63 0.70
396 0.57 0.62 0.69
without CA (Gießen)
97 0.69 0.71 0.71
108 0.68 0.71 0.71
197 0.61 0.66 0.67
258 0.54 0.59 0.65
For small D149 loadings, the calculated values FFint,calc are well in line with FFint,exp. Furthermore, the experimentally observed weaker decay of the fill factor with the dye loading in cells containing CA is confirmed: a decay from 0.71 to 0.69 is calculated for the cells with CA, compared to a decrease from 0.71 to 0.65 for the samples without coadsorbate. Because the change of Voc with the dye loading was identical for cells with or without CA, this result shows that the decay of the fill factor with absint was caused by the decay of β. For larger amounts of dye, the cells show smaller internal fill factors than expected according to the model. A possible reason for this may be that the rate of recombination in the model is approximated by an empirical expression including a constant (i.e., voltage-independent) recombination rate constant kr (cf. eq. (32)). How-ever, in the present cells kr may have depended on the voltage, since there was evidence for additional recombination at lower voltages in the cells with high dye loadings. A more precise description should include an energy-dependent average rate constant of recombination rather than a constant one, as for example suggested by Wang et al..86
5.3.5 Series Resistance
The comparison of the internal and external fill factors given in Table 10 revealed that the efficiency of the DSCs analyzed in this chapter was significantly limited by the se-ries resistance Rseries. In Figure 46, the various contributions to Rseries are illustrated for a sample cell (adsorption time of 120 minutes, without CA) as a function of the d.c. cell current density flowing through the cell at different d.c. bias voltages.
Figure 46: Graphs illustrating the different EIS-derived contributions to the series re-sistance of a sample ZnO/D149 solar cell. Rd: diffusion resistance of the electrolyte, Rs: resistance of the FTO-coated glass substrate, RPt: resistance of the Pt-coated counter electrode.
In the current range relevant for solar cell operation (positive J), the resistancesof the substrate and of the counter electrode (Rs and RPt) presented the main contributions to the total series resistance. For negative J, on the other hand, the diffusion resistance Rd
of ions in the electrolyte became increasingly dominant. The constant distance between the curves showing Rd and Rd+Rs in Figure 46 demonstrates that the resistance of the FTO-coated glass substrate was constant in the current range investigated. The diffusion resistance of the electrolyte, however, clearly increased towards negative J, while the counter electrode resistance tended to grow with increasing positive J.
Comparing the counter electrode resistance for all different preparation conditions stud-ied in this chapter (Figure 47), there was a tendency of an increase of RPt with the
ad-sorption time, which was particularly pronounced for cells without cholic acid. RPt was clearly smaller in samples with coadsorbate compared to those without CA.
Figure 47: Charge-transfer resistance at the electrolyte/counter electrode interface vs.
the d.c. cell current density for ZnO/D149 solar cells with (filled symbols) or without (open symbols) coadsorbate cholic acid. Curves belong to one solar cell each and are representative of the behavior of samples with identical adsorption conditions. Assign-ment of colors as in previous figures.
The diffusion resistance of the electrolyte (Figure 48) exhibited a similar dependence on adsorption time and coadsorbate as RPt: increasing tads tended to increase Rd and sam-ples with CA showed a somewhat lower diffusion resistance than those without coad-sorbate. Since RPt and Rd reflect properties of the electrolyte and the electrolyte/counter electrode interface, their dependence on the adsorption time indicates that the D149 molecules partially desorbed from the ZnO surface and dissolved in the redox electro-lyte when the DSCs were filled with the solution. This may have affected the transport of charges between counter electrode and dye-sensitized ZnO. Once dissolved in the electrolyte, it is likely that some of the dye molecules adsorbed onto the surface of the Pt/FTO counter electrode, hindering charge transfer between electrolyte and counter electrode.
Figure 48: Diffusion resistance of the electrolyte (0.1 M I2 and 1 M TPAI in 4:1 eth-ylene carbonate:acetonitrile) of ZnO/D149 solar cells with (a) or without (b) cholic acid, determined by fitting the impedance spectra.
In a laboratory project performed by J. Schmidt under the supervision of the author,287 the influence of D149 molecules intentionally added to an I-/I3- electrolyte (identical composition as used in this thesis) on charge transport through the electrolyte and charge transfer at the interface to Pt-coated FTO/glass were investigated. Current-voltage characterization and electrochemical impedance spectroscopy of symmetrical Pt/electrolyte/Pt cells showed that with increasing concentration of D149 (between 0 M and 5 mM) the diffusion coefficient of I3- decreased by a factor of about 1.5, while the charge-transfer resistance of the Pt/electrolyte interface increased by a factor of almost 20. These results strongly support the hypothesis that the variations of RPt and Rd ob-served for cells with different dye loadings in the present work were caused by different amounts of dye that desorbed from the ZnO film and dissolved in the electrolyte. In the cells containing CA, D149 may have been more stably bound to the ZnO surface, so that less dye molecules were present in solution and at the counter electrode surface and RPt was smaller than in cells without coadsorbate. Repeated J-V measurements of the present samples four weeks after preparation (see chapter 9.2) showed a significant de-crease of the short-circuit photocurrent in the cells without CA, while those with coad-sorbate in fact exhibited an increase of Jsc, supporting the suggestion that the stability of the D149 attachment may have been lower in the cells without coadsorbate. As larger amounts of dye aggregates were present in the samples without CA, a weaker
attach-ment to ZnO of D149 molecules in aggregates compared to monomeric D149 molecules could be the reason for the observed differences.